Problem #1: Section 1.3, exercise 16 (a,c,e,f). Remember to define your
predicates and the universe of discourse.
Problem #2: Section 1.3, exercises 38 and 48
Problem #3: Section 1.4, exercises 8 and 22 (a,b)
Problem #4: Section 1.5, exercise 34
Problem #5: Section 1.5, exercise 48
Homework #2 - Due Wednesday 9/18
Topics: Functions, sequences and summations (Rosen Ch. 1.6-1.8).
Problem #1: Section 1.6, exercise 20.
Problem #2: Section 1.6, exercise 56.
Problem #3: Section 1.7, exercises 18(a,d) and 22.
Problem #4: Section 1.8, exercises 8(a,c) and 26.
Problem #5: Section 1.8, exercises 46 and 48.
Homework #3 - Due Wednesday 9/25
Topics: Algorithms and integers (Rosen Ch. 2.1-2.3).
Problem #1: Section 2.1, exercise 4.
Problem #2: Section 2.1, exercise 22.
Problem #3: Section 2.2, exercise 16.
Problem #4: Section 2.3, exercise 16.
Problem #5: Section 2.3, exercise 26.
Non-Homework 1 - for optional
exam review only; not to be turned in
Topics: Integers and matrices (Rosen Ch. 2.4-2.6).
Problem #1: Section 2.4, exercises 2 (c, e), 8 (c,d), and 12 (a, b, c).
Show
your work!
Problem #2: Section 2.5, exercise 8. (Hint: Look at the proof of Theorem
3, which proves that an inverse exists if 144 and 233 are relatively prime.)
Problem #3: Section 2.5, exercise 18.
Problem #4: Section 2.6, exercise 3 (a, b, c).
Problem #5: Section 2.6, exercise 18.
Homework #4 - Due Wednesday 10/9
Topics: Proof techniques and mathematical induction (Rosen Ch. 3.1-3.2).
Problem #1:Section 3.1, exercise 2.
Problem #2: Section 3.1, exercise 14.
Problem #3: Section 3.1, exercise 32.
Problem #4: Section 3.2, exercise 2.
Problem #5: Section 3.2, exercise 38.
Homework #5 - Due Wednesday 10/16
Topics: Recursion and correctness (Rosen Ch. 3.3-3.5).
Problem #1:Section 3.3, exercise 4 (a,b,c).
Problem #2: Section 3.3, exercise 22. Note: For part (c), you
can assume that only the variable x is used in the polynomials.
Problem #3: Section 3.4, exercise 6. Note: Your algorithm does
not have to be optimal. However, if you want to, you can use the result
that xy mod m = [ (x mod m) (y mod m)] mod m. (That is, you can either
perform all of the multiplications, then take the mod, or apply mod before
each multiplication, meaning that the size of the numbers to be multiplied
are smaller.)
Problem #4: Section 3.5, exercise 4.
Problem #5: Section 3.5, exercise 12.
Homework #6 - Due Wednesday 10/23
Topics: Counting and the Pigeonhole Principle (4.1-4.2).
Problem #1: Section 4.1, exercises 4, 8, and 12
Problem #2: Section 4.1, exercise 46
Problem #3: A chess set has 16 black pieces and 16 white pieces: 8 pawns,
2 rooks, 2 knights, 2 bishops, a king and a queen of each color. The pieces
of a given type and color are interchangeable . Given a fixed orientation
for the chess board, and given that the white pieces will be placed in
the bottom two rows and the black pieces will be placed in the top two
rows, how many different ways are there to place the chess pieces? (For
example, the lower left square will always contain one of the two white
rooks, so there are two different choices for which rook to place in this
position)
Problem #4: Section 4.2, exercises 2 and 18.
Problem #5: Section 4.2, exercise 34.
Homework #7 - Due Wednesday 10/30
Topics: Permutations and probability (4.3-4.4, part of 4.5)
Problem #1: Section 4.3, exercise 24(a,b). Hint for part (a)
- try thinking about how many strings do not contain an "a."
Problem #2: Section 4.3, exercise 24(c,d).
Problem #3: Section 4.4, exercises 2, 4, 6, and 8.
Problem #4: Section 4.4, exercise 18.
Problem #5: Section 4.5, exercises 2 and 6.
Homework #8 - Due Wednesday 11/6
Topics: Recurrence relations (5.1, 5.3)
Problem #1 - 5.1.4 (b, e, g)
Problem #2 - 5.1.8
Problem #3 - 5.1.18
Problem #4 - 5.3.14
Problem #5 - 5.3.6
Non-Homework 2 - for optional
exam review only; not to be turned in
Topics: Probability, Generalized Permutations and Combinations, Inclusion-Exclusion
(4.5-4.6, 5.5-5.6).
Problem #1: 4.5.18
Problem #2: 4.5.20
Problem #3: 4.5.28, 4.5.30
Problem #4: 4.6.2, 4.6.6, 4.6.8
Problem #5: 5.5.8, 5.5.16
Homework 9 - Due Wednesday 11/20
Topics: Relations (6.1-6.4).
Problem #1: Section 6.1, exercise 4(a,b,d).
Problem #2: Section 6.1, exercise 28(a,c,e).
Problem #3: Section 6.2, exercises 8 and 10, and the following question:
In exercise 6.2.10, suppose there are m records in the first table and
n records in the second table. Also suppose that fields 3-5 serve as a
composite key for the first table, and fields 1-3 serve as a composite
key for the second table. (a) What is the minimum number of records
(not fields) in the result of applying the J3 operation? (b) What is the
maximum
number of records in the result of applying the J3 operation?
Problem #4: Section 6.3, exercises 8(b,c,e) and 14.